Six pure phenolic compounds (hydroquinone, thymol, carvacrol, butylated hydroxyanisole, gallic acid, and octyl gallate) were tested for their minimum inhibitory concentration (MIC) and minimum bactericidal concentration (MBC) against several strains of Staphylococcus aureus isolated from dairy and meat products. In addition, S. aureus reference strains (American Type Culture Collection) for antimicrobial studies and/or isolated from human infections and outbreaks of food poisoning were included in the study. Of the compounds tested, octyl gallate and hydroquinone were the most effective against S. aureus (mean MIC values of 20.89 and 103.05 μg/mL, respectively) and carvacrol and thymol the least (mean MIC values of about 413 μg/mL). The mean MBC values were 40.84, 194.37, 417.46, and 581.90 μg/mL for octyl gallate, hydroquinone, carvacrol, and thymol, respectively. Meat isolates were more resistant than those of dairy origin to hydroquinone, gallic acid, and octyl gallate, as well as to penicillin G (used as a control of the methodology used); gallic acid and penicillin G showed the highest differences in MIC values between the groups of strains (about 10 and 200 times, respectively). On the other hand, when we tested the isolates included in each group of strains (dairy, meat, and other/mixed sources) we only detected significant differences (p < 0.05) among dairy and isolates from other/mixed sources for hydroquinone and thymol, respectively. However, strains of meat origin exhibited significant differences among each other (p < 0.05) to most of the phenolic compounds tested (hydroquinone, carvacrol, gallic acid, and octyl gallate). The relationship between MICs and MBCs for each of the phenolic compounds tested suggested a bactericidal mechanism of action against S. aureus. Gallic acid and octyl gallate exhibited the highest antioxidant capacity and thymol and carvacrol the lowest. So, octyl gallate is an agent with both antimicrobial and antioxidant properties, which would be of interest to use in the food industry.